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In this paper, analytical solutions of response functions for rectangular resonators are investigated in time domain. Emphasis is placed on the study of electromagnetic field coupling to a 3-D cavity through a small circular aperture. The time-dependent parts of the resulting modal Green's functions exhibit typical behavior that is inherent in all resonating/oscillating linear physical systems: namely, they fulfill oscillating ordinary differential equations at any point of the considered resonator. Their solutions contain transient and steady-state parts. The transient parts of the response functions will become important for electromagnetic compatibility tests in particular of modern digital high-speed electronics.